Topological rainbow trapping, concentration and guiding in graded elastic valley phononic crystal plate

Topological structures are well known for their robust and unidirectional wave transportation in acoustic and elastic communities. The rainbow effect in metamaterials is also promising for applications such as buffers, filters, wavelength-division multiplexing devices, and etc. In this work, the combination of topology and rainbow effect, i.e., topological rainbow, is investigated. The topological rainbow trapping and rainbow concentration in valley topological phononic crystal plates with gradient substrate are observed both numerically and experimentally. The topological rainbow guiding, where the elastic waves are guided in a spatial-spectral way, is also presented. The precise control of elastic waves with topological protection and in spatial-spectral way provides a convenient path to design future phononic devices such as elastic energy harvesters, signal storages, and communication devices.